Mathematics anxiety has increasingly been recognized as a problem in the classroom over the past few years. In this vein, Barroso et al [1]. noted that math anxiety has increased with the increased volume of nonroutine problem-solving techniques in the classroom. This increase was accelerated when the National Council of Teachers of Mathematics placed nonroutine problem-solving at the top of their list of priorities in 1980 in an Agenda for Action. The authors then described the teacher's role in alleviating the problem. This role involved creating a nurturing, caring atmosphere in the classroom. The contribution made to this nurturing attitude was a specific suggestion concerning the use of Transactional Analysis in the approach to the affective domain in teaching mathematics. Beilock and Maloney [2], in an earlier paper, had described the role in more detail. Gabriel et al, elaborated by saying the effective teacher should encourage students, encourage them to ask questions, provide them with ample feedback, and be patient. Beilock and Maloney [2], also suggested the teacher should be aware of the possible negative effects the testing process may have on the anxiety level and avoid inflexible or insensitive behavior. In addition, he mentioned an emphasis on problem-solving as an essential part of the mathematics curriculum. Also, he encouraged avoidance of sex-role stereotyping, describing mathematics as a male domain.
Mathematics anxiety is an experience of mental disorganization, panic, and fear that prevents a person from learning mathematics. In an increasingly technological society, knowledge of mathematics is vital to the pursuit of many existing and emerging occupational fields. This knowledge is used in areas such as natural sciences, engineering, business, and the social sciences. Marshman and Marshman [3] stated that in spite of the importance of mathematics, intellectually capable students identified as experiencing mathematics anxiety avoid taking mathematics courses in high school and college and consequently restrict the range of careers from which they may choose to those that do not require quantitative skills. In addition, advancement even in non-technical careers is severely hampered by the fear of data, budgets, percent, and numbers
The literature describes a variety of causes of mathematics anxiety. Bicer et al [4] identified eight causes, which they placed into three categories. The causes were divided into those which were student-related, those which were teacher-related, and those that were teaching-related. The student-related causes were divided into (1) lack of confidence and (2) negative student attitude. The teacher-related were divided into (1) teacher bias and (2) authoritarian teaching. The teaching-related were divided into (1) lack of variety, (2) lack of relationship with the real world, (3) emphasis on memorization, and (4) emphasis on speed. The literature often states or suggests that much of the source of mathematics anxiety is related to the teachers and the teaching of mathematics.
It would therefore seem appropriate to attempt to isolate specific teacher behaviors that cause or alleviate mathematics anxiety. In this study, a systematic review will be conducted to isolate those specific behaviors. It is hoped that such a study will contribute to the understanding of mathematics anxiety, its causes, and cures [5]. The problem for this study, then, was to determine what specific teacher behaviors affect mathematics anxiety in mathematics students. The expanding research literature on mathematics anxiety has spawned the need to integrate the findings of existing research studies on this topic. An important step to meet this need was taken when the researchers used the methods of meta-analysis to synthesize the findings regarding the nature, effects, and remedies of mathematics anxiety. A perusal of Coronado [6] meta-analysis provided these observations: Most of the mathematics anxiety research has been done at the college level. The problem for this study, then, was to determine what specific teacher behaviors affect mathematics anxiety in mathematics students at the selected school in the United States. The level of math anxiety was examined in entire classes.
Causes of mathematics anxiety
Low mathematics achievement, low general ability, and avoidance of mathematics in high school were correlated with mathematics anxiety. These characteristics may be self-perpetuating in that low ability leads to low performance, which leads to the dislike of mathematics, which leads to mathematics anxiety, which leads to mathematics avoidance, which leads to low mathematics achievement, according to the study by Dowker [7]. Math anxiety often began in the elementary grades, where stress on memorization of rules, timed tests, student competition in the classroom, and limited discussion of mathematics problems tended to create stress and tension in students. In a study by Finlayson [8] elementary teachers indicated that math anxiety developed for them because of an inadequate math background; sarcastic, inadequate, or impatient teachers; low grades in math; and parents who were displeased with their grades in math. Different sources of mathematics anxiety were collected by Bailey [9] from autobiographies of math-anxious adults. The sources of math anxiety were time pressure, humiliation, emphasis on the right answer, and working in isolation. Most math-anxious people can probably trace the cause of their anxiety to some of the following: timed tests, overemphasis on right answers and the right method, working at the blackboard in front of peers, lack of acceptance of nontraditional problem-solving methods, and such negative counseling as, 'You won't need this,' or 'You aren't smart enough to learn this" . Assadi et al [10] an expectation times values model of achievement motivation. He believed that course selection and not innate ability to be the critical factors that are related to gender-role socialization (e.g., parents, teacher beliefs), anticipated tasks or roles in relationship to the child's self-concepts of his or her mathematical abilities. A stressful learning environment has also been shown to be a critical cause of mathematics anxiety for females. Schools sometimes fail to provide environments appropriate to females’ learning. Gender studies show that females learn better in cooperative rather than competitive class climates and in single-sex mathematics classes.
Further, mathematics anxiety sets the stage for a downward spiral of diminished mathematics success while lowering self-esteem. The decline in mathematics achievement causes avoidance of mathematics courses, especially advanced classes which, in turn, limits a student's choice in selecting college majors and future careers. Because mathematics anxious females discontinue mathematics courses earlier in their education than males, many women function as "underachieving adults", females "who do not achieve similar professional accomplishments as their male counterparts". Our society is increasingly dependent on mathematics literacy; for instance, the ten highest-ranked jobs for the 21st century in America will be related directly to mathematics, and of the ten fastest-growing occupations, eight are science, mathematics, or technology related. In addition, it is forecast that jobs requiring mathematics and science skills will increase by 5.6 million by 2008. Unfortunately, mathematics anxiety acts as a screen that filters females from many occupations.
Effects of mathematics anxiety
Joët [11] conducted groundbreaking research on the effects of mathematics anxiety on working memory. They attempted to integrate psychometric studies of mathematics anxiety with mathematical cognition studies that focused on mental representations and processes used in mathematics performance. Working memory is the system for conscious, effortful mental processing. The study found that working memory capacity is negatively associated with mathematics anxiety. That is, as mathematics anxiety increases, working memory capacity decreases. The original study shows that individuals with high mathematics anxiety demonstrate small working memory spans that lead to an increase in reaction time (time required to correctly answer a question).
In fact, a prior study of working memory showed that for carrying versus non-carry arithmetic problems, high mathematics anxiety students can take as much as three times longer to correctly answer than low mathematic anxiety students. As mathematics concepts become more difficult, beyond the retrieval of facts, students must rely more on working memory. As this occurs, students manifest other mathematics anxiety effects such as failure to focus on the task at hand and responding quickly to problems to the detriment of accuracy. Both these effects can be seen as a coping mechanism that allows minimum time for anxiety-producing mathematics situations and as a precursor to avoidance of mathematics courses. Chopra et al [1] results are consistent with processing efficiency theory, a model of general anxiety effects. This theory hypothesizes that general anxiety disrupts working memory processes, and the anxious students are distracted by off-task thoughts.
The effect of teacher behavior
Response consequences served several purposes, one of which was as a motivator. One can be motivated to learn or motivated to avoid a topic. “A great deal of human behavior is activated by events which become threatening through association with painful experiences”. A counselor interviewed by Gunderson et al [13] explained math phobia by saying “If you don’t feel safe, you won’t take risks. People who don’t trust math may be too wary of math to take risks” (p. 58). The teacher was the force of power that set the class tone. The authors emphasized this; the teacher’s choice of exercises, materials, and assignments evoke meanings the teacher may not have intended. For example, a teacher may make a child go to the blackboard to work out a problem in an attempt to encourage students to be prepared and to let them ‘show off their knowledge. But for the unprepared, the shy, or the struggling to learn, it can be a humiliating and debilitating experience. Mathematics knowledge of preservice teachers was found to have a significant relationship to their learning of mathematics pedagogy but was not related to their teaching performance in a five-week field experience. These results seem to be inconsistent with those of Hoorfar and Taleb [14]
Hoorfar and Taleb [14] found teachers' knowledge of mathematics during their final year of college was positively related to their students' mathematics achievement. The researchers showed that a reduction in mathematics anxiety was possible by comparing the results of a pre-test of mathematics anxiety using the Math Anxiety Rating Scale (MARS) and the MARS as a post-test before and after the mathematics methods course was conducted. These findings were in agreement with the results reported by Li et al [15] in a study of student teachers; researchers found that teachers with high anxiety scheduled fewer minutes per day of mathematics instruction than non-anxious student teachers. In research conducted using first-year elementary teachers in grades 2 through 5, it was reported that those teachers with the highest levels of mathematics anxiety were from 10 to 15 lessons behind their peers who had less mathematics anxiety. Maloney and Beilock [17] concluded that the most anxious teachers avoid teaching math even though they may be as competent in math instruction as their less anxious peers. One way to reduce mathematics anxiety was for teachers to take a mathematics methods course.
This method of mathematics anxiety reduction was recommended for preservice elementary teachers by Namkung et al [18]. In this study, the teachers enrolled participated in small group activities that emphasized the use of manipulatives as teaching aids, classroom lectures, and discussion, and each participated in a five-week practice teaching experience. The results of the study showed a reduction in mathematics anxiety had occurred when the pre-test MARS scores and the post-test MARS scores of students were compared. As the result of a study on mathematics anxiety in relation to mathematics preparation and perceived adequacy of preparation. The authors recommended that an integrated staff development course containing materials in both methods of teaching mathematics and the content of mathematics be required.
Namkung et al [18] noted that improved behavior management skills are not the only way to create a nurturing and caring environment for mathematics anxious students. Teachers can express their care by their choice of pedagogical practices and better serve all students in the way they structure and teach mathematics. Powerful and engaging lessons of interest to the students are effective in creating a productive and nurturing environment. When students are actively engaged in the lesson, there are fewer student misbehaviors and fewer distractions for the anxious mathematics student; thus, allowing learning and understanding to occur. Namkung et al [18] recommend various teaching strategies to keep students actively engaged in the learning of mathematics, such as cooperative groups and authentic assessments. Interestingly, the students in this study suggested pedagogical practices that agree with those recommended by the Namkung et al [18]. Both recommended small group instruction, standards-based "constructivist" pedagogy, and authentic assessments that orient students towards learning rather than performance. When instructional strategies were employed that emphasized learning and understanding developed mathematics ability, students perceived a more welcoming environment and experienced decreased mathematics anxiety.
Namkung et al [18] feel that attitudes can be transmitted from teachers to their students and therefore feels that if mathematics anxiety can be reduced in prospective teachers, the benefit will extend to the students. She feels that an elementary mathematics methods course, if taught correctly, can lower mathematics anxiety. The first step is to tell the students that developing positive attitudes toward mathematics is one goal of the course. By discussing attitudes, students find out that they are not alone with their feelings about mathematics. The second step is to organize students into small groups so that no one person takes all the responsibility for finding an answer. The third step is to encourage a variety in methods of solving problems. "The awareness of many ways of approaching mathematical problem solving helps alleviate some of their mathematics anxiety ."The next step is to be sure that students see the meaning behind mathematics. Discovering that every rule has a reason, and understanding that reason helps develop self-confidence. Next, help the student to see the importance of not teaching solely from a textbook, and finally, put less emphasis on tests as evaluation for the course.
Olson & Stoehr., [19] discussed some different causes of math anxiety during the high school years. First was the instructor exhibiting angry behavior: "Instructors exhibited anger when asked for further clarification of problems." As bad as these examples reflect upon the K-12 teacher, Orbach & Fritz., [20] research showed that things continue in college. Here too, the instructor was often characterized as insensitive and uncaring. Orbach & Fritz [20] noted at the college level several new categories of events that can lead to math anxiety. Some instructors were noted for their dislike of the class level: "Some instructors were offended at having to teach entry-level mathematics classes and vented their frustrations on students." For the first time, age discrimination appears: "Instructors showed insensitivity to older students than the traditional 18-to-22-year-old bracket when these students expressed anxiety about returning to school after many years" Lastly, Orbach & Fritz [20] noted covert instructor behavior that may lead to math anxiety: "Instructors sighed in a demeaning manner. Instructors avoided eye contact with students".
Pizzie & Kraemer [21] noted math language as a cause of math anxiety. Math uses symbols that can hide the full meaning unless one is fluent in the language. This covert method used in instruction can be just as impacting as covert behavior. The researchers found all of the above factors to be the roots of "anxiety-producing responses. The problem-solving approach. This approach focuses largely on teaching basic problem-solving skills and provides a more realistic motivational context in which specific problem-solving techniques can be taught so as to help learners apply mathematics to practical daily problem-solving situations. The use of the problem-solving approach in mathematics demands extensive preparation and the development of ways to maintain an east medium of classroom control and perhaps the ability to envision teaching goals. The technique may not, however, guarantee solutions to problems but may serve as a guide in the problem-solving process.
Role of intervention strategies
Since a decrease in mathematics anxiety can increase achievement in mathematics, it is essential to determine positive interventions for mathematics anxiety. The literature is not in agreement about which interventions are appropriate. Namkung et al [18] did a meta-analysis of quantitative mathematics-anxiety studies to integrate findings. One task was to examine treatments to alleviate mathematics anxiety. In some of these studies, classroom interventions, which include the use of computers and calculators, small group instruction, and "heuristic"1 instruction, did not seem effective in reducing mathematics anxiety at the high school and postsecondary levels, nor did they produce improved mathematics performance. In contrast to Namkung et al [18], other studies suggest that classroom interventions, such as small group instruction and heuristic instruction, can reduce mathematics anxiety.
Pletzer et al [22] writes that some researchers show a reduction of mathematics anxiety when a standards-based manner of teaching mathematics is used, one that shifts from a basic skills pedagogy to constructivist mathematics pedagogy. The study found that providing facilitative environments where teachers are patient, encouraging, and supportive of students’ learning styles tends to reduce mathematics anxiety. As stated by the authors “the methods used to teach mathematics skills may affect whether a student feels successful and develops mathematical self-confidence” and suggest less rote mathematics learning and emphasis on more meaningful understanding of mathematics material. Similarly, the Radisic et al, (2015) recommends the use of various instructional techniques, such as using cooperative groups to promote student learning and utilizing alternate assessments, to provide a challenging yet nurturing mathematics environment. Cooperative group work, in particular, has been found to have a positive impact in the classroom. The cooperative atmosphere of small groups is more beneficial for girls than for boys. It increases their enjoyment of mathematics, their level of thinking, and duration of time on task in mathematics classes [23]. In cooperative groups, students, especially females, have a greater opportunity to be heard and also to learn by participating in a more collaborative and democratic academic environment.
The study carried out by Radisic et [24] noted that learning groups support students and spur their enthusiasm for mathematics. These changes in attitudes caused by learning mathematics in small groups have a positive effect on reducing females’ mathematics anxiety and increasing mathematics achievement. Teachers “must use practices that will best enable underserved and underrepresented groups, particularly females and people of color, to learn math”. On the other hand, studies using psychological treatments to relieve mathematics anxiety show decreased mathematics anxiety and appear to be related to better mathematics performance. Since these forms of intervention do not include any mathematics instruction or practice, “it would appear that lower mathematics competence cannot be offered as a simple, wholesale explanation for all the performance decrements associated with mathematics anxiety”.
Radisic et [24] found a significant reduction of mathematics anxiety with the behavioral treatment of systematic desensitization. Systematic desensitization combines muscle relaxation exercises with imagining exercises. Mathematics anxious people receive gradual exposure to mathematical concepts and situations that cause them distress. Then, using learned relaxation techniques, they practice relaxing in these uncomfortable situations. Another proven psychological intervention is counseling aimed at restructuring false beliefs and building self-confidence in mathematics ability. Through counseling, students may understand that mathematics anxiety is a learned behavior. Such awareness may help them work through their fears and begin to build self-confidence in their ability to achieve in mathematics.
The authors explained that mathematics anxiety is an experience of mental disorganization, panic, and fear that prevents a person from learning mathematics. The treatment for mathematics anxiety proposed by these researchers suggested that allowing individuals to relive and thereby overcome their experience of powerlessness and personal inadequacy with mathematics helps them to reduce mathematics anxiety. These investigators designed a workshop to be used for this purpose. It was neither a mathematics class nor a therapy group; it was a combination of both. This kind of treatment supports model, as well through the investigation and implementation of a treatment to overcome mathematics anxiety, suggested that it is healthier and more productive if the focus in the mathematics class is on mastery of mathematics and the development of positive feelings toward it, rather than on the amount of material covered.